Analysis of Contribution of Muscle Synergies on Sit-to-Stand MotionUsing Musculoskeletal Model

Qi An1, Yuki Ishikawa1, Junki Nakagawa1, Hiroyuki Oka2,Hiroshi Yamakawa1, Atsushi Yamashita1 and Hajime Asama1

Abstract— Recently, declining physical ability of elderlypeople has become an extremely important social issue. Toimprove their daily living activities, the standing-up motionis emphasized in this study as an important daily motion.Synergy analysis is applied to the standing-up motion toextract four important groups of muscle activations (synergies).Furthermore, the effect of synergies on body movement iscalculated based on a musculoskeletal model of the human body.Results suggest that the first synergy works as preparation ofthe motion by pulling the ankle and flexing the hip. The secondsynergy controls the joint moment of the hip and knee jointsto raise the hip and move the center of mass forward. Thethird synergy controls the ankle joint according to movementof the center of mass. The last synergy stabilizes the posturechange from a seated to a standing position. Our findings implythat it is important to train those functional muscle activity toenhance the ability of standing-up motion.

I. INTRODUCTION

In this paper, the standing-up motion is analyzed based onmuscle synergies, and the effects of synergies are elucidatedfrom a musculoskeletal model of the human body.

Recently, the number of elderly people has increasedrapidly. Many have suffered from degraded quality of lifebecause of decreased physical ability from aging or disease[1]. In addition, such circumstances impose increased welfarecosts or physical and mental burdens to informal care givers[2]. To solve those problems, it is important to enhance thephysical activity of elderly people. Particularly, the humanstanding-up motion is an important motion because manydaily activities are distracted or become impossible withoutthe standing-up motion [3].

For assisting the standing-up motion, we previously devel-oped an assistive system that consists of a bed and a supportbar system [4]. The system has a force sensor on the barthat encourages system users to use their remaining forceto stand up if the measured force from the sensor is lessthan a threshold value. It generates a fixed trajectory that isextracted from a nursing specialist to lead people if the forceis greater than the threshold.

This system can lead people to stand up, but it mightstrengthen the dependence of users on the system, whichimplies that functional mobility cannot be fully improved

1 Q. An, Y. Ishikawa, J. Nakagawa, H. Yamakawa, A. Ya-mashita, and H. Asama are with Department of Precision Engineer-ing, The University of Tokyo, 1138656 Tokyo, Japan anqi atrobot.t.u-tokyo.ac.jp

2H. Oka is with The 22nd Century Medical and Research Center,Graduate School of Medical and Faculty of Medicine, The University ofTokyo, 1138655, Tokyo, Japan

solely by assisting the deficit force or leading people to acertain trajectory. To improve their physical ability, compen-sation of deficient function alone should not be specificallyexamined, but the muscles which actuate body joints mustbe analyzed.

Muscle strength training is known only to be effectivewhen people use their muscles in the same posture as theyperform the training [5]. Additionally, it has been suggestedthat people should train several muscles rather than a singlemuscle [6]. Results from those previous studies imply thatimprovement of physical ability depends on the exerciseitself (context of the motion) and that it has less effect thanusing simple muscle strength training.

Therefore, it is necessary to analyze the standing-upmotion itself to ascertain the muscle activities included inthe motion to enhance physical ability. Developing effectivetraining for functional mobility would be useful if thestanding-up motion were divisible into several groups ofmuscle activations.

Regarding reports of earlier studies that have analyzedhuman standing-up motions, the standing-up motions canbe divided into four phases based on body trajectoriesand movement of the center of mass [7]. In addition, ourprevious study [8] extracted groups of muscle coordinationfrom standing-up motions, and their effects on standing-upmotion have been identified through a neural network modelrepresenting the human musculoskeletal model. However,this neural network model does not consider anatomicalcharacteristics of the human body.

This study measures muscle activation, body trajectory,and reaction force from standing-up motion and elucidatescoordinated muscle activations. Our objectives are to clarifyrelations between extracted muscle activations and jointmovement through a musculoskeletal model that employsanatomical characteristics.

II. IDENTIFICATION OF SYNERGY AND ITSCONTRIBUTION TOWARD BODY MOVEMENT

A. Synergy Model

In this study, synergy analysis is used to extract groupsof muscle activations from human motion. The idea ofsynergy analysis was proposed originally by N. Bernstein[9]. It states that people use groups of coordinated severalmuscle activations (synergy) to control their redundant body:the body has more muscles than the number of controlledjoints. As described in this paper, we use a model in which

muscle activation during motions is approximated by linearsummation of several synergies [10].

Equation (1) shows a synergy model used in our study.In the model, d kinds of muscles are observed and muscleactivation is expressed as a matrix M. Each column ofM consists of a vector m(t), which expresses d musclesactivation at time t. The element of this vector mj(t) denotesmuscle activation of j-th muscle at time t as in Eq. (2). Tmax

represents the total time of muscle observation.

M ∼=N∑i=1

ciwi(t− ti), (1)

M = [m(1),m(2), · · · ,m(Tmax)]

=

m1(1) · · · m1(t) · · · m1(Tmax)m2(1) · · · m2(t) · · · m2(Tmax)

.... . .

.... . .

...md(1) · · · md(t) · · · md(Tmax)

.(2)

This model includes the assumption that the observedd muscle activations are approximated by N synergieswi=1,2,··· ,N . wi comprises vectors (wi

1(t), wi2(t), · · ·wi

d(t)).Each synergy wi

j is the time-varying synergy activation ofj-th muscle in i-th synergy. The actual muscle activationM is expressed as a linear summation of synergy wi, withactivation coefficient ci and time delay ti.

Figure 1 presents an example of the synergy model. Inthis example, d kinds of muscle activation (Fig. 1(a)) are ex-pressed as the superposition of three synergies (w1,w2,w3).Three synergies have different activation patterns (Fig. 1(c)).In Figs. 1 (a) and (c), the horizontal axis indicates theduration of time in human movement whereas the verticalaxis shows the observed muscle activations. People mustcontrol their activation coefficient (c1, c2, c3) and time delay(t1, t2, t3) to achieve a complex human motion. Colouredarrows in Fig. 1 (b) show duration of three synergies.The height of each arrow indicate activate coefficients andblack arrows show time delays for synergies. It depictsthat synergies have sufficient timing to be activated withweighting coefficient.

B. Extraction of Synergies

Decomposition algorithm [11] is used to decompose ob-served muscle activation to synergy patterns, activation co-efficient, and time delay. The algorithm uses multiplica-tive update rules to minimize the squared errors betweenobserved muscle activation (M) and approximated patterns(∑N

i=1 ciwi(t − ti)). The algorithm firstly selects common

synergy patterns from several trials. Afterwards, it deter-mines activation coefficient and time delay for each trial.

To ascertain the number of synergies which can suffi-ciently express human standing-up motion, we change thenumber of synergies to be extracted to evaluate the accuracyof the model and thereby explain human standing-up motion.

Cross-validation method is used to evaluate the modelaccuracy. Observed EMG data from several different motionsis divided into (X − 1) groups of training data and the

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Fig. 1. Synergy Model

remaining 1 group of test data. Synergy patterns are extractedfrom training data and are evaluated in test data.

The coefficient of determination R2 is used to evaluatethe degree to which the extracted synergies can explain theobserved EMG data. R2 are calculated in different numbersof synergies. A sufficient number of synergies is chosen torepresent the observed muscle activation.

To ascertain the optimal number of synergies to be ex-tracted, one-factor repeated measures analysis of variance(ANOVA) is applied to assess the effect of the number ofsynergies on the accuracy of the model. When there is astatistically significant difference, the Tukey–Kramer test isused for post hoc tests. For this study, the significance levelis set as p = 0.05.

C. Effect of Synergies toward Body Trajectory

To analyze the effect of extracted synergies toward bodyjoints, the ratio of joint angle change is calculated whenextracted synergies are put into a musculoskeletal model.Figure 2 presents our methodology to calculate the changeof joint angles.

Human body movement is calculated from the muscularforce exerted on the joint and the body posture when force isexerted. Additionally, it is known that muscle tendon force isaffected by the muscle length (= joint angles) and the speedof muscle contraction (= angular velocity). Therefore, theinputs of the musculoskeletal model are muscle activationand body posture (joint angle and angular velocity) at timet, from which it is possible to compute the human bodyposture at the next time t+ dt. First, initial joint angles andangular velocities are input to the musculoskeletal model.Later, the calculated body posture is put recurrently intothe musculoskeletal system to calculate the next posture.The link models with dashed blue lines and solid redlines respectively show the initial posture and movementgenerated from the input synergy. The change between the

initial posture and generated movement by input synergyis examined specifically in this study. As described herein,musculoskeletal model of human lower limbs is developedusing SIMM (MusculoGraphics Inc.).

In addition, the starting point of four phases is calculatedfrom the reaction force and body trajectory to elucidateeffects of synergies in terms of the kinematics of the hu-man standing-up motion. Figure 3 indicates the four phasesdefined in the previous study [7].

Phase I is the beginning phase of the standing-up motion;people bend the trunk firstly. The starting point of PhaseI is defined as the beginning of the shoulder’s horizontalmovement. It is determined as the time at which the velocityof shoulder exceeds vI. During Phase II, people rise their hipto transfer the momentum forward. Therefore, the beginningof Phase II is the time when people rise their hip from a seat;it is determined when reaction force from hip becomes lessthan FII. Phase III is the extension phase to lift up the trunk;the start of Phase III is decided as the time when maximumankle flexion is observed. The last phase is the stabilizationphase, at which time people finish their motion and stabilizethe posture. The beginning of Phase IV is determined whenthe vertical shoulder position becomes the highest.

III. MEASUREMENT OF STANDING-UP MOTION ANDSYNERGY ANALYSIS

A. Setup

In this research, three joints, such as extension and flexionof hip, knee, and ankle are examined to investigate howextracted synergies affect the body trajectory. Figure 4 (a)presents the joint angles considered in this study. Joint anglesare defined from the red solid lines, and the direction of redarrows indicates joint flexion. Because the human standing-up motion is performed on the sagittal plane, the movementof only the right body part is specifically examined.

Specifically regarding those muscles which actuate the hip,knee, and ankle joints, eight muscles are measured. Figures 4(b)–(c) present a view of the measured muscles from frontand back views: biceps femoris (BF), rectus femoris (RF),vastus lateralis (VL), vastus medialis (VM), semitendinosus(SE), tibialis anterior (TA), peroneus longus (PL), and thegastrocnemius (GAST). Those muscles are chosen based onthe anatomical viewpoint according to whether those musclesaffect body joints. Following are the flexion and extensionof each joint and muscles connected to those joints.

• Hip Extension: BF• Hip Flexion: RF, VL, VM

Musculoskeletal

System

Initial Posture

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Fig. 2. Computation of Joint Angle from Musculoskeletal System

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Fig. 3. Phase Clarification in Standing-up Motion

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Fig. 4. Musculoskeletal System

• Knee Extension: RF, VL, VM• Knee Flexion: BF, SE, GAST• Ankle Extension: TA• Ankle Flexion: PL, GASTFigures 4 (d)–(e) show measured body positions to cal-

culate the body trajectory of the standing-up motion. In all,seven markers were attached to the right and left as is, backsacral, right knee, ankle, heel, and toe. Joint angles and thecenter of mass are also calculated using SIMM. The segmentlength of our musculoskeletal model is ascertained by a staticpose in which people stand still and spread their arms wide.

B. Participants

One healthy man participated in our experiment (26 yearsold, 1.77 m height, 79 kg weight). Before the start of theexperiment, consent was obtained in compliance with theethics committee of the Graduate School of Medicine andFaculty of Medicine, The University of Tokyo.

C. Procedure

In this study, people were asked to stand up from a chairthat was 0.45 m high and which had neither an arm restnor a backrest. A subject was asked to place feet shoulder-width apart and to have arms crossed in front of the chestin order not to use their arms to stand up. The subject wasasked to stand-up in comfortable speed. In our measurementexperiment, 72 standing-up motions were obtained.

D. Signal Processing

To perform synergy analysis, all EMG data were sub-tracted by the mean and filtered using 200 Hz low-pass and5 Hz high-pass filters. In addition, all data were rectified anda smooth filter was applied as in Eq. (3). In the equation,mi(t) is the i-th measured muscle activation and m′

i(t) is thefiltered data. Later, data were downsampled to 200 Hz. EMGdata were normalized to 0–1 based on maximum voluntarycontraction of each muscle.

m′i(t) =

∑t′=49t′=−50 mi(t− t′)

100. (3)

Body trajectory data was obtained in 200 Hz. For thepost process of body trajectory data, spline interpolation wasapplied in case of data gap. Afterwards, 10 Hz low-pass filterwas applied. Reaction force was measured in 64 Hz and wasfiltered with 25 Hz low-pass filter and resampled to 200 Hz.

IV. RESULTS

A. Data Analysis

Synergy analysis was performed on observed 72 standing-up motions. The obtained data were divided randomly intosix groups with 12 data (five training groups and one testgroup). The coefficient of determination was computed fortest group in different numbers of synergies (1–7) extractedfrom the training group. This cross validation method wasrepeated seven times for seven test groups. After the numberof synergies was determined, the extraction of synergies wasperformed for all 72 data.

B. Determination of Number of Synergies

The mean of the coefficients of determination is calculatedfrom obtained 72 trials of standing-up motion. Figure 5portrays a change of mean and standard deviation accordingto the numbers of synergies. According to the results ofANOVA, a significant difference was found in the coefficientof determination among numbers of extracted synergies(p <0.05; F=248.3). When a post-hoc test was conductedfor the neighboring number of synergies, a statisticallysignificant difference was found between one and two, twoand three, and three and four, which demonstrates that thecoefficient of determination is saturated when the numberof synergy is four. Therefore the number of synergies to beextracted is chosen as four.

C. Extraction of Synergies

Table I presents average time delay and its standarddeviation of extracted four synergies. Activated muscles inextracted synergies, and its effect on joints are shown in Fig.6. Solid red lines and dashed yellow lines respectively showextension and flexion of the joint.

The first synergy (w1) starts from the early time ofthe standing-up motion (0.36±0.68 s); the biceps femoris(BF), vasutus medialis (VM), tibialis anterior (TA), peroneuslongus (PL) are activated. The second synergy (w2) beginsat the middle of the motion (0.80±0.28 s); the rectus femoris(RF), biceps femoris (BF), vastus lateralis (VL), vastusmedialis (VM), peroneus longus (PL) are activated. Thethird synergy (w3) also starts at the middle of the motion(0.94±0.29 s); the biceps femoris (BF), vastus lateralis (VL),vasuts medialis (VM), tibialis anterior (TA) are activated.The fourth synergy (w4) begins at the last of the motion(1.39±0.66); the biceps femoris (BF), semitendinosus (SE),gastrocnemius (GAST), peroneus longus (PL) are activated.

D. Phase Division

Obtained data are divided into four phases based on thedefinition of the previous study [7]. In this study, vI and FII

were set to 0.1 m/sec and 10 N. Table II presents the averagestart time of each phase and its standard deviation.

E. Change of Joint Angle from Synergy

Table III shows changes of joint angles when extractedsynergies are put into the musculoskeletal model. Positiveand negative values respectively denote the direction ofextension and flexion. w1 mainly flexes the hip, and extendsknee and ankle joints. w2 extends the hip and knee joints,and flexes ankle joint. w3 and w4 extends all joints.

Figure 7 shows examples of muscle synergies and mea-sured body movement in the standing-up motion. Figure 7(a) portrays time series of hip, knee, and ankle joints, andthe center of mass in horizontal and vertical directions. Four

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TABLE ITIME DELAY FOR EACH SYNERGY

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Mean Time Delay [s] 0.36 0.80 0.94 1.39STD Time Delay [s] 0.68 0.28 0.29 0.66

vertical solid lines in the figure show the start of each phase.The solid red line, dashed black line, and green broken linerespectively show angles of the hip, knee, and ankle. Theblue line with blue circle markers shows the change of thecenter of mass in the horizontal direction. The blue line withblue triangle markers shows the change of the center of massin the vertical direction. The left y axis of the graph showsthe joint angles [deg], the right y axis shows the center ofmass [m], and the x axis shows time [s].

Figure 7 (b) represents extracted synergies in a squarewhose rows are time-series of different muscle activation.The abscissa shows time. Activations are expressed in grayscale: the brighter, the more activations are observed. Figure7 (c) shows the measured muscles. Each synergy has timedelay and the order of synergies start is w1, w2, w3, andw4 in this example.

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Fig. 6. Extracted Synergies

TABLE IISTART TIME OF EACH PHASE

I II III IVMean Start Time [s] 0.78 1.1 1.4 2.2STD Time Delay [s] 0.16 0.17 0.17 0.22

TABLE IIICONTRIBUTION OF EACH SYNERGY

w1 w2 w3 w4

Hip [%] -6.5 112.5 92.7 66.8Knee [%] 30.9 74.0 125.8 53.0Ankle [%] 20.5 -296.0 63.9 44.1

V. DISCUSSION

The first synergy w1 begins before Phase I, which is thestart of standing-up motion defined by results of a previousstudy [7]. Particularly, the result of both activation agonistmuscle (TA) and antagonistic muscle (BF) shows that theypull their ankle by stiffening the ankle joint. In addition, thisis the only synergy which flexes the hip joint. It starts tobend before the predicted movement.

The second synergy w2 has more activations than othersynergies; it continues from the middle of Phase I toPhase III. This synergy controls joint moment of hip andknee by activations of both agonist and antagonistic muscles.In addition, extension of hip and knee joints raises the hipto move the center of mass forward.

The third synergy flexes the ankle joint. It is presumed tocontrol the movement of the center of mass from Phase IIto Phase III. At the same time, it extends the hip and kneejoints to lift up the upper body.

The last synergy continues from Phase III to IV to extendall joints, but its activations are fewer than those of the thirdsynergy w3. That fact implies that this synergy stabilizes theposture rather than lifting up the upper body. In Phase IV,posture must be stabilized against the vertical movement ofcenter of mass from a seated to a standing position.

These four synergies suggest an important trainingmethodology for standing-up motion. If people need to trainthe first motion preparation and hip bending motion, theyneed to enhance co-activation of back of thigh (BF) andfront shank (TA). Similarly, the second synergy implies thenecessities to train front thigh to rise their hip. In order totrain body extension, simultaneous activation of front thigh(VL and VM) and front shank (TA) will be needed. Onthe other hand, enhancement of antigravity muscles (PL andGAST) is essential for training of posture stabilization. Basedon synergies which are related to functional body movementof standing-up motion, muscle training strategy is proposed.

Although synergies were extracted only from one subject,the synergy analysis is applicable to several subjects to elu-cidate their similarities and differences. In this methodology,joint movements were calculated without consideration of thereaction force to the foot, but the reaction force was includedto investigate the motion of pulling of the ankle or movementof the center of mass to their feet.

Our study used eight muscles to express standing-upmotion due to the constraints that only outer muscles aremeasurable by surface EMG, although other important mus-cles affect the motion or body trunk, such as the psoasmuscles. However, those inner muscles are barely measurablefrom surface EMG sensors. Therefore, the future direction ofour study is to employ an estimation algorithm to compute

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the activation of inner muscles from kinematic data.Additionally, the standing-up motion will be measured

under various circumstances. This study measures the motionin the same circumstances, but it is known that movementspeed, chair height, and the usage of arm and back rests willinfluence the motion. Therefore, the synergy analysis will beapplied to other data recorded under different circumstancesto elucidate variant and invariant structures of synergies.

VI. CONCLUSIONS

Four synergies in standing-up motion were extracted andits effects on each joints were calculated. Those resultssuggest that each synergy works as motion preparation, risinghip and movement of center of mass forward, flexion ofthe ankle joint and lifting up upper body, and stabilizationof posture after standing-up motion. In addition, muscleco-activation included in extracted synergies implies newtraining strategy for improvement of standing-up motion.

ACKNOWLEDGMENTThis work was in part supported by Japan, MEXT KAK-

ENHI, Grant-in-Aid for Scientific Research (B) 24300198,and Grant-in-Aid for JSPS Fellows 248702.

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